×

zbMATH — the first resource for mathematics

On resolvable spaces and groups. (English) Zbl 0837.22001
A topological space \(X\) is said to be resolvable if there exist two disjoint dense subsets of \(X\). The author proves that every uncountable \(\omega\)-bounded topological group is resolvable as well as every homogeneous space containing a non-trivial convergent sequence. It is also shown that under Booth’s lemma, the weight of every non-discrete irresolvable topological group is at least \(2^{\aleph_0}\). Some open problems are posed in the article, one of which asks for the existence of an irresolvable topological group that is not extremally disconnected.
Some results of the paper have also been announced by W. W. Comfort, O. Masaveu and H. Zhou at the IX. Summer Topological Conference, 1993.

MSC:
22A05 Structure of general topological groups
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54H11 Topological groups (topological aspects)
20K45 Topological methods for abelian groups
PDF BibTeX XML Cite
Full Text: EuDML